(530d) A Novel Mathematical Model for Short-Term and Medium-Term Scheduling of Multipurpose Batch Plants

Rakovitis, N., University of Manchester
Li, J., The University of Manchester
Zhang, N., University of Manchester
Short-term scheduling of multipurpose batch plants has gained a lot of attention during the past three decades [1-3]. Different mathematical models such as discrete-time models [4-5] and continuous-time models including sequence-based models [8-9], process slot-based models [6], unit-slot models [7], global event-based models [10-11], and unit-specific event-based models [12-15] have been developed. The scheduling horizon is represented using time points, batches, slots, or event points. The computational efficiency and solution optimality of all these models largely depend on the number of time points (batches, slots, or event points) that are required to generate the optimal solution. In other words, reducing the required number of time points (batches, slots or event points) could lead to substantial decrease in computational expense. The advantages of the unit-specific event-based modelling approach have been well established in the literature [13-14], which often requires fewer number of event points than discrete-time, process slot-based, and global event-based modelling approaches. However, it seems that the proposed unit-specific event-based models are still computationally inefficient especially for large-scale industrial problems since a high number of event points are still required. Furthermore, a consumption task is always sequenced with any production task in different units related to the same state regardless of whether this consuming task consumes materials either from a specific production task or from storage tank [15-16]. Although this unconditional sequencing has been mitigated in recent two models [15-16], they may either lead to large model sizes which require excessive computational effort to generate the optimal solution or even sub-optimality and infeasibility.

In this work, we develop a novel unit-specific event-based formulation for short-term scheduling of multipurpose batch plants, where production and consumption tasks related to the same state are allowed to take place at the same event, which could significantly reduce the number of event points that are required to generate optimal solution. The definition of recycling tasks from Li and Floudas [14] and recycling states is employed to avoid infeasibility arising from allowing recycling tasks to take place at the same event points with their related consumption tasks with the same recycling states. To further reduce the number of event points that are required, we introduce a new binary variable to explicitly identify the specific production task or storage that provide materials to a consumption task. We sequence a consumption task only with the related specific production task that provides materials to this consumption task, not all related production tasks. Additionally, when a task consumes materials that already exist in storage, we do not need to sequence it with any production task. To illustrate the capability of our proposed model, we solve a number of examples that are well established in the literature. The computational results demonstrate that the proposed model significantly reduces the number of event points that are required and decreases the model size. As a result, our proposed model requires less computational time to generate the optimal solution compared to the existing models. We then incorporate our proposed model into the rolling horizon framework [17] to solve medium-term scheduling of large-scale industrial batch plants. The comparison results demonstrate that better profit could be generated with our proposed model compared to that of Janak et al. [17].


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